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M. Zubkov ITEP Moscow 2010

The vicinity of the phase transition in the lattice Weinberg – Salam Model and Nambu monopoles. M. Zubkov ITEP Moscow 2010 B. L. G. Bakker, A. I. Veselov, M. A. Zubkov, J. Phys. G: Nucl. Part. Phys. 36 (2009) 075008; A.I.Veselov, M.A.Zubkov, JHEP 0812:109,2008;

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M. Zubkov ITEP Moscow 2010

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  1. The vicinity of the phase transition in the lattice Weinberg – Salam Model and Nambu monopoles M. Zubkov ITEP Moscow 2010 B. L. G. Bakker, A. I. Veselov, M. A. Zubkov, J. Phys. G: Nucl. Part. Phys. 36 (2009) 075008; A.I.Veselov, M.A.Zubkov, JHEP 0812:109,2008; A.I. Veselov, M.A. Zubkov, proceedings of LATTICE2009; M.A.Zubkov, arXiv:0909.4106 Phys.Lett.B684:141-146,2010

  2. Abstract The lattice Weinberg - Salam model without fermions is investigated numerically for realistic choice of bare coupling constants correspondent to thevalue of the Higgs mass . On thephase diagram there exists the vicinity of the phase transition between thephysical Higgs phase and the unphysical symmetric phase, where the fluctuationsof the scalar field become strong. In this region Nambu monopoles are dense andthe perturbation expansion around trivial vacuum cannot be applied. Out of thisregion the ultraviolet cutoff cannot exceed the value around 1 Tev. Within the fluctuational region the maximal value of the cutoff is (The data is obtained on the lattice )

  3. Fields • Lattice gauge fields (defined on links) • Fundamental Higgs field (defined on sites) Lattice action Another form:

  4. Phase diagram at constant (U(1) transition is omitted) lines of constant physics Physical phase Transition surface Unphysical phase Tree level estimates:

  5. Along the line of constant physics if we neglect gauge loop corrections to One loop weak coupling expansion: bare and are increased when the Ultraviolet cutoff is increased along the line of constant physics

  6. Realistic value of Weinberg angle The fine structure constant The majority of the results were obtained on the lattices The results were checked on the lattices

  7. phase diagram line of constant renormalized Physical phase Condensation of Nambu monopoles Unphysical phase

  8. phase diagram

  9. The renormalized fine structure constant Right – handed lepton Wilson loop The simple fit approximates V(R) better than the lattice Coulomb potential

  10. The potential

  11. The potential

  12. Renormalized fine structure constant

  13. Evaluation of lattice spacing Z – boson mass in lattice units: (the sum is over “space” coordinates of the Z boson field) are imaginary “time” coordinates

  14. Ultraviolet cutoff along the line of constant renormalized Condensation of Nambu monopoles Unphysical phase Physical phase

  15. in lattice units Fit for R = 1,2,3,4,5,6,7,8 Phys.Lett.B684:141-146,2010 Phase transition

  16. in lattice units Fit for R = 1,2,3,4,5,6,7,8 The results yet have not been checked on the larger lattices Phase transition

  17. Higgs boson mass in lattice units (the sum is over “space” coordinates of the Z boson field) are imaginary “time” coordinates Higgs boson mass in physical units:

  18. Phase transition at

  19. Phase diagram at constant lines of constant physics Physical phase Transition surface Unphysical phase

  20. Effective constraint potential

  21. Potential barrier Hight

  22. Minimum of the potential at

  23. NAMBU MONOPOLES (unitary gauge) NAMBU MONOPOLE Standard Model NAMBU MONOPOLE Z string

  24. Worldsheet of Z – string on the lattice NAMBU MONOPOLE WORLDLINE

  25. Susceptibility Nambu monopole density Phase transition

  26. Susceptibility Nambu monopole density Phase transition

  27. Percolation Transition Nambu monopoles Nambu monopoles Line of constant renormalized fine structure constant Ultraviolet cutoff

  28. Excess of link action near monopoles Excess of plaquette action near monopoles Phase transition

  29. Phase diagram at constant lines of constant physics Physical phase Transition surface Unphysical phase

  30. Previous investigations of SU(2) Gauge - Higgs model Lattice action At realistic value of Weinberg angle The fine structure constant is For we have

  31. Cutoff (in Gev) in selected SU(2) Higgs Model studies at

  32. Conclusions We demonstrate that there exists the fluctuational region on the phase diagram of the lattice Weinberg – Salam model. This region is situated in the vicinity of the phase transition between the physical Higgs phase and the unphysical symmetric phase of the model. In this region the fluctuations of the scalar field become strong and the perturbation expansion around trivial vacuum cannot be applied. ?

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